An integrated stochastic inventory model with lead time decisions

This paper considers an integrated inventory system with one supplier and one buyer under the assumption of stochastic lead times and constant unit demand. A supplier's replenishment lead-time is composed of setup, production and transportation times; all times are assumed to be stochastic. The randomness of each lead-time can be determined so that it can be reduced at a cost or be increased by reducing current investment levels in excessively invested processes. Under a lot-for-lot policy, two integrated inventory models, which have order quantity, reorder level, and lead times as decision variables, are developed. We then investigate cost savings for joint expected total cost per unit time by lead-time decisions (JETCUT) and by non-lead-time decisions (JETCUT NON). Some sensitivity analyses will be conducted with respect to various relevant inventory parameters.